Trump's senior team huddled privately to focus on a period of transition planning. In addition to Christie, the group included Republican National Committee Chairman Reince Priebus, Alabama Sen. Jeff Sessions, Vice President-elect Mike Pence, daughter Ivanka Trump's husband Jared Kushner, and others.

Speaking on NBC's "Today" show Thursday, Christie said he does not believe the George Washington Bridge lane closure scandal will cloud his future.

Trump to Nation: ‘I Will Not Let You Down'

Donald Trump, speaking from New York City, addressed his supporters after he was elected president of the United States. “It’s been what they call a historic event,” Trump said. “But to be really historic we have to do a great job and I promise you that I will not let you down.”

(Published Wednesday, Nov. 9, 2016)

The Republican said he's not committed to doing anything in a new administration. He says his job is to get Trump through the transition and he'll talk with the president-elect if there's any job that Trump wants him to do.

Christie refused to say if he was interested in a specific job with the new administration.

“I have a job to do to help get the administration ready. If there’s some role for me that I want to do, and that the president-elect wants me to do — we’ve known each other for 14 years — we’ll talk about," he said.

Sources told NBC News a number of Trump's most loyal supporters were being considered for positions in his presidential cabinet, among them former New York City Mayor Rudy Giuliani and former House Speaker Newt Gingrich.

Giuliani is being looked at for attorney general, the sources said. Giuliani told CNN Thursday: "I certainly have the energy, and there's probably nobody who knows the Justice Department better than me."

However, that's a change of tune from Wednesday when Giuliani told The New York Times, "I'm not interested in returning to government.

Gingrich, an author of the Contract with America in the mid-1990s while in the Congress representing Georgia, could be a candidate for secretary of state.

WATCH: Donald Trump's Victory Speech

Donald Trump gave a victory speech early Wednesday morning after securing enough electoral votes to win the presidency.

(Published Thursday, Nov. 10, 2016)

Other possible names that have been put forward: retired Lt. Gen. Michael Flynn for defense secretary or national security adviser; Steve Mnuchin, Trump's finance chairman, for treasury secretary, and Lew Eisenberg, the Republican National Committee finance chairman, for commerce secretary, three campaign advisers told NBC News. Flynn would need a waiver from Congress because he has not been retired from the military for seven years as would be required.

Priebus, who was a staunch Trump defender, could be the chief of staff, according to NBC News.

Helping to vet the names are the conservative Heritage Foundation and Trump's running mate Pence.

The White House said Trump's team will start working directly with federal agencies this week on the transition.

President Obama’s Full Post-Election Remarks

President Barack Obama addressed the nation on Nov. 9, after congratulating president-election Donald Trump in the early morning hours for his win. Watch his full remarks here.

(Published Wednesday, Nov. 9, 2016)

Trump's team will start getting briefings related to the Defense Department, State Department, Treasury Department and other agencies. The briefings will include budget details, flow charts for staff and other information.

Officials at those agencies will start speaking regularly to Trump team members to facilitate the handover of power in January. And Trump's team will start creating policy teams that will work out of government-provided offices near the White House.

The White House also said the Obama administration will host two "exercises" involving multiple agencies to help familiarize Trump's team with government practices and systems for responding to domestic emergencies.

The White House said Trump's team will start working directly with federal agencies this week on the transition.

Trump's team will start getting briefings related to the Defense Department, State Department, Treasury Department and other agencies. The briefings will include budget details, flow charts for staff and other information. Officials at those agencies will start speaking regularly to Trump team members to facilitate the handover of power in January. And Trump's team will start creating policy teams that will work out of government-provided offices near the White House.

The White House also said the Obama administration will host two "exercises" involving multiple agencies to help familiarize Trump's team with government practices and systems for responding to domestic emergencies.